Axioms in philosophy are not axioms until they are proved upon our pulses: we read fine things but never feel them to the full until we have gone the same steps as the author.

In addition, the teaching of theories from axioms, or some close imitation of them such as the basic laws of an algebra, is usually an educational disaster.
ivor grattanguinnessOne of the most important axioms is, that as the quantity of any commodity, for instance, plain food, which a man has to consume, increases, so the utility or benefit derived from the last portion used decreases in degree. The decrease in enjoyment between the beginning and the end of a meal may be taken as an example.
william stanley jevonsEthical axioms are founded and tested not very differently from the axioms of science. Truth is what stands the test of experience.
Albert EinsteinThe life of the law has not been logic; it has been experience... The law embodies the story of a nation's development through many centuries, and it cannot be dealt with as if it contained only the axioms and corollaries of a book of mathematics.
Holmes, Jr., Oliver WendellOne of the central axioms of extreme programming is the disciplined use of regression testing during stepwise software development.
The life of the law has not been logic; it has been experience... The law embodies the story of a nation's development through many centuries, and it cannot be dealt with as if it contained only the axioms and corollaries of a book of mathematics.
Pointed axioms and acute replies fly loose about the world, and are assigned successively to those whom it may be the fashion to celebrate.
If we wish to express our ideas in terms of the concepts synthetic and analytic, we would have to point out that these concepts are applicable only to sentences that can be either true of false, and not to definitions. The mathematical axioms are therefore neither synthetic nor analytic, but definitions. ...Hence the question of whether axioms are a priori becomes pointless since they are arbitrary.
Philosophy complains that Custom has hoodwinked us, from the first; that we do everything by Custom, even Believe by it; that our very axioms, let us boast of Freethinking as we may, are oftenest simply such Beliefs as we have never heard questioned. Nay, what is Philosophy throughout but a continual battle against Custom; an everrenewed effort to transcend the sphere of blind Custom, and so become Transcendental?
thomas carlyle"Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs.
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